.B 41 

.fl35 
'Opy 1 



UNIVERSITY OF CALIFORNIA. 






RIVERSIDE ADDRESSES. 




1891 



BERKELEY: 

PUBLISHED BY THE UNIVERSITY. 
1892. 



■•MpMl' 



LB 41 (^ctJ^yi'.v^-..a>^^ 

P35 [UNIVERSITY BULLETIN No. ST.] 

Copy 1 



ADDRESSES ,^^„^. 

FEB 7 t9n 



DELIVERED BEFORE THE 



CALIFORNIA TEACHERS' ASSOCIATION, 

AT RIVERS] 



DECKIMBER psr— 
BY 

Professors in the University of California. 




1. Bducational Progress in California. 

Prof. Martin Kellogg. 

2. The Social Sciences as Aids in Teaching History. 

Prof. Bernard Moses. 

3. The Past and Present of Elementary Mathematics. 

Prof. Irving Stringham. 

4. Physics in Secondary Schools; some Aspects of the Present 

Situation. Prof. Frederick Slate, 



BERKKIvEY: 

PUBI.ISHED BY THE UNIVERSITY. 
1892. 



V* 



Printed at the State Printing Office, Sacramento. 
A. J. Johnston, Superintendent. 



EDUCATIONAL PROGRESS IN CALIFORNIA. 

By Professor Martin Kei.i.ogg, 

Acting President of the University of California. 



California was admitted into the Union in 1850. Its 
preliminary Constitutional Convention was held a year 
earlier. The years of its State life may be roughly 
divided into decades, of which only four are now com- 
plete. This division of time will afford a convenient 
method of grouping the events of our educational 
history. 

I. We go back, first, to the beginnings of our school 
system. The foundation for this system was laid in 
1849, in the Constitutional Convention at Monterey. 
An inviolable school fund was then established. Article 
IX of the Constitution said: "The Legislature shall 
encourage, bj^ all suitable means, the promotion of 
intellectual, scientific, moral, and agricultural improve- 
ment." Section 4 of the same article directs the Legis- 
lature to care for a permanent fund for the support of 
a university " for the promotion of literature, the arts 
and sciences.'^ 

But there were schools antedating 1849. As early 
as October, 1847, the Town Council of San Francisco 
provided for the erection of a small school-house, and 
in April, 1848, it was occupied, with Thomas Douglass 
(a Yale graduate) as teacher (salary |i,ooo a year). 
There were at first six pupils; the number increased to 
thirty-seven, then suddenly dropped to eight. The 



4 Riverside Addresses. 

dropping off was due to the mining excitement which 
swept so many off to the interior, and among them 
teacher Douglass. 

During these years, private schools were opened b}^ 
Messrs. Marston, Williams, and Pelton. 

The first school law was passed by the Legislature of 
1850-51. Any district drawing money from the school 
fund must maintain a school at least three months in 
the year. This law provided for the establishment of 
high schools. It allowed religious schools to receive 
aid from the fund. 

San Francisco had had, in 1850, a free public school, 
independent of any State law. The Common Council 
established it, and John C. Pelton was at its head. 

According to the report of the first State Superin- 
tendent, in 185 1, there were about six thousand chil- 
dren in California between the ages of 4 and 18. 

II. Let us now pass on to the neighborhood of the 
sixties. In 1858 there were over forty thousand chil- 
dren of school age, of whom less than one half attended 
the public schools. In 1855, religious schools had been 
shut out from the school fund. In 1861, an attempt 
to admit them again to its benefits was defeated. Much 
interest, during this first decade, had been shown in 
developing the school system. The patrons of the 
schools still paid rate-bills. The schools were not y^t 
in a condition at all satisfactory to the State Superin- 
tendents, as is evinced by their reports. 

I turn now to another line of development, viz.: the 
beginnings of college instruction. If I give this a large 
place, I plead in excuse the " personal equation," as my 
environment has given me a special interest in college 
work. 



Educational Progress in California, 5 

In i860, the College of California began college 
instruction in Oakland. It was not the first college on 
this coast. Other colleges, or "universities," were 
earlier in the field. But those other institutions 
depended chiefly on what we call preparatory classes. 
Whoever aspired to a college degree must take his 
advanced studies as he could get them, in company 
with scholars of lower grade. The one noteworthy 
distinction of the College of California was this : It had 
no preparatory school work to look after; it had a 
Faculty exclusively devoted to college studies. Its 
standard was the standard of the Eastern States. This 
made a marked advance upon any previous effort. 

From the first 3^ears of California's statehood, a few 
educated men had ooked forward to such a college. 
In 1849, a charter was sought through the first Legis- 
lature. The bill authorizing such charters was passed, 
leaving the special application to be made to the 
Supreme Court. A financial basis of $20,000 was to 
be a prerequisite. A cluster of men, afterward inter- 
ested in the College of California, had obtained a 
promise of certain tracts of land and applied for a 
charter, but defective titles defeated the application. 
This was in 1850. 

In 1853, Henry Durant came to do educational work 
in California, and started a preparatory school in Oak- 
land. He interested a few college men in his enter- 
prise, which, from the outset, aimed at the building up 
of a college. A small building was rented at a high 
price, and his school began with three pupils. In 1855 
the three had increased to sixty. 

The same year a charter for a college was obtained, 
the Trustees named being Fred. Billings, Sherman Day, 
S. H. Willey, T. D. Hunt, M. Brumagim, E. B. Wals- 



6 Riverside Addresses. 

worth, J. A. Benton, K. McLean, H. Durant, F. W. 
Page, R. Simson, A. H. Wilder, and S. B. Bell. 

These Trustees had very definite aims. One of these 
was to unite the religious people of the State in an 
effort to establish a first-class college, which, like Yale 
and Princeton, should be Christian in tone, but practi- 
cally unsectarian. Starr King was a member of the 
Board, and after him Horatio Stebbins. The very 
breadth of their scheme increased the difficulties of the 
Trustees. Devoted denominationalists could not be 
deeply interested, and waited for an institution all 
their own. 

Another definite aim was to place the college on a 
high footing by obtaining for a President some distin- 
guished man from the East. Dr. Horace Bushnell was 
almost secured. He was one of the loftiest souls in the 
whole land, and was deeply interested in education. 
He came to this State for his health, and spent much 
time in looking up a good college site. With health 
regained, he yielded to the importunities of his old 
church, and was lost to California. Drs. Shedd and 
R. D. Hitchcock in turn declined the offers of the 
Trustees. 

Thrown back upon their own efforts, the Board 
moved forward. They secured a college site, now 
occupied by the University at Berkeley, and dedicated 
it on April i6, i860. In the summer of that year the 
college began its work in Oakland. Its first Freshman 
Class had been trained by Dr. Durant. The first pro- 
fessors chosen were Durant and Kellogg, the latter of 
whom began work in 1861. Prof Bray ton took certain 
classes, but gave most of his energies — too unspar- 
ingly — to the school left b}" Dr. Durant. 

Thus, after the first ten or twelve years of California's 



Educational Pi^ogress in California. 7 

life, we see the full establishment of a common school 
system, and the beginning of separate, determined 
college work. 

III. We pass on to the seventies, to the close of a 
second decade. What advances have these years to 
show? 

On the part of the schools, a great expansion and a 
higher level. Early in the sixties, increased provision 
was made for a school fund. John Swett became State 
Superintendent, and argued strongly for a special State 
tax. Such a tax was laid in 1864. The year ending 
with June, 1867, "marks the transition period of Cali- 
fornia from rate-bill common schools to an American 
free school system." The Superintendent records this 
fact with pardonable pride. A school library sj^stem 
was provided by the law of 1866, and put into success- 
ful operation. The average salary of male teachers 
was reported as $77 a month; of female teachers, $64. 
Fifty thousand children were enrolled in the schools. 
From 1 86 1 to 1871 there were eight State Institutes. 
At the third of these, called in San Francisco by Super- 
intendent Swett, there was an attendance of four hun- 
dred and sixty-three. In 1867, five hundred teachers 
were present. These Institutes were of much value in 
giving the teachers an esprit de corps, and in influenc- 
ing school legislation. In 1869, the State tax was 
increased to 10 cents on each $100. 

On the side of the higher education there was an 
advance from the college to the university. As in 
the case of the college, the university idea had long 
been cherished: how it should take shape, was a ques- 
tion to be determined by events. As has been men- 
tioned, the Constitution of 1849 made reference to a 



8 Riverside Addresses. 

university, and enjoined on the I^egislature the protec- 
tion of funds granted for such an institution. In 1856, 
Superintendent Hubbs urged the establishment of a 
university. His successor, Superintendent Moulder, 
discussed the subject at large. 

In 1853, Congress granted to this State seventy-two 
sections of land " for the use of a seminary of learning.'' 
Also, ten sections of land for a public building fund. 
In 1862, by the Act known as the Morrill Act, Con- 
gress gave to the State one hundred and fifty thousand 
acres of public land for an Agricultural and Mechanic 
Arts College. This donation was accepted in 1864. In 
the previous year the Legislature appointed a Commis- 
sion to report a plan for a university, the chairman 
being Prof. J. D. Whitney. The scheme elaborated by 
this Commission was very different from the plan finally 
adopted. In 1866 a Board of Directors was established 
for an "Agricultural, Mining, and Mechanic Arts Col- 
lege." The next year the Directors located the college 
in Alameda County. 

In the same year, 1867, came a proposition from the 
College of California, looking to a larger and broader 
institution, a real university. The Trustees of the 
college had tried faithfully to expand their own insti- 
tution; but the process was slow, and the financial 
prospects unfavorable for the early fulfillment of their 
hopes. They had a fine property in Oakland, and the 
magnificent site of one hundred and sixty acres at 
Berkeley. They had established a high college stand- 
ard. Through their seven years of actual college 
work at Oakland, and through the very successful 
Alumni gatherings of men from Eastern institutions, a 
wider interest in college instruction had been developed. 
The Trustees now offered to turn over their property 



Educational Progress in California. 9 

and good- will to a State University, with the condition 
that the University should maintain certain colleges of 
science "and an academical college," "all of the same 
grade and with courses of instruction equal to those of 
Eastern colleges." This offer was accepted by the 
Board of Directors of the Agricultural College. An 
act to create and organize the University of California 
was introduced in the lower house of the Legislature 
March 5, 1868, by John W. Dwindle, and approved 
March 23d. We call that our Charter Da3^ 

The College of California continued its instruction 
till the summer of 1869, and then became merged into 
the Universit3\ The first appointees to professorships 
in the University were Dr. John Le Conte and Prof. 
Kellogg. Dr. Joseph Le Conte and others soon fol- 
lowed. The first University Class entered in 1869. In 
1870 there were two classes, and young women had 
already been admitted on an equal footing with young 
men. 

The end of this second decade, therefore, is marked 
by the complete establishment of a free public school 
system ; and by the estabhshment of a State Univer- 
sity, taking up and much enlarging the previous work 
of the college. New attention was given to the claims 
of the natural sciences, to the demand for training for the 
scientific professions, and to the bearing of education 
on industrial occupations. Military training, the only 
condition imposed with the national grant, became a 
part of the students' education. Our State took a step 
in advance of any other in making tuition in its Uni- 
versity absolutely free. 

IV. The third decade brings us to the eighties. 
In these years the public school system gained in 



10 Riverside Addresses. 

efficiency. In his report for 1875, State Superintendent 
Bolander notes an important advance in furnishing aid 
to the smaller school districts. Some of them had 
fallen short of the minimum of three months : now 
the distribution was more equal and helpful. He 
argues in this report for a special and extended course 
in the University for teachers. 

During this decade there was a local political cyclone, 
which for awhile overturned the calculations of the 
old parties. It brought about, in 1879, a new Consti- 
tutional Convention, whose proceedings interest us in 
one or two points. First, high schools were left out of 
the schools to be supported by the State tax. Any 
community wishing for a high school must itself meet 
the expense. This omission of the high school, in 
the series of schools provided by the State, has had 
a chilling effect on the higher education. Common 
schools were free, the University was free ; but how 
were pupils to get from the one to the other? The 
larger cities bridged the chasm without much hesita- 
tion by establishing high schools at their own expense. 
The smaller towns and country districts were slow to 
assume the burden. 

Notwithstanding these difficulties, the University 
maintained its high standard of admission. It could 
not lower the requirements without taking a long and 
fatal step backward. 

That Constitutional Convention took another step 
which was not adverse, but favorable to the State Uni- 
versity. Article IX, Section 9, declared: "The Uni- 
versity of California shall constitute a public trust, and 
its organization and government shall be perpetually 
continued in the form and character prescribed by the 
organic act creating the same." In that radical Con- 



Educational Progress in California. 11 

vention it was decided that the University was some- 
thing not to be uprooted. 

V. And now we come to the nineties. 

The common schools have prospered as never before. 
More really well-educated teachers have been found in 
the profession. As a profession, teaching has become 
a more honorable and a more permanent occupation. 
We have now three normal schools instead of one. 
Teachers' Institutes have been made a part of the 
school system, and they have been attended with 
increasing interest, even enthusiasm. The whole ma- 
chinery of the school system has been elaborated and 
made more efficient. The teachers have shown increas- 
ing devotion to their work, and the best of them have 
found appreciation in the community at large. The 
one weak point in the system, showing itself chiefly 
in the larger cities, is the method of choosing Boards 
of Education. 

The unfortunate chasm between the common school 
and the University has been more and more regretted, 
and there have been strenuous efforts to bridge it over. 
Years ago the schools were authorized to add some- 
what to their courses, in the direction of the scientific 
requirements of the University. The last Legislature 
passed two bills for the establishment of high schools: 
the one for county high schools, the other for city or 
town high schools and union district high schools. 
The burden of maintenance was still to be local, but 
provision was made for putting the question before the 
people, and for lev3dng the needful tax. These laws 
have spurred up a considerable number of communities, 
and the work of establishing high schools is now going 
forward with the most favorable prospects. 



12 Riverside Addresses. 

The standard aimed at in these high schools is most 
encouraging. As one object in estabUshing them was 
to pave the way to the University, the requirements of 
the University have been cheerfully met. These re- 
quirements do not hinder, but rather help, in fixing a 
curriculum of most value to students who take no 
further course. It is always borne in mind that only 
a minority are to take a college course, but this minor- 
ity must not be debarred from going forward. 

A special feature of the last decade has been the 
attainment of a uniform standard. This has been 
brought about by a system of accrediting. Our Uni- 
versity was not the first to devise this system: Michigan 
was already using it. But we may claim to have made 
the system more thorough than we found it. More 
pains is taken here than anywhere else to visit, advise, 
and encourage each one of the main departments of 
instruction in every school applying for recognition. 
The results have been very satisfactory, and the circle 
of accredited schools is constantly widening. Nearly 
thirty are already on the list. 

Another gain is seen in the call for a longer curricu- 
lum in the high schools. Californians have been fond 
of short cuts and the briefest possible courses of study. 
But the State is less in a hurry than it was. It is 
coming to see that haste makes waste, that the basis of 
a broad and solid scholarship cannot be laid by a fever- 
ish urgenc}^ A few high schools have already provided 
a four years' course. If this can become general, it will 
react on the grammar schools, and bring about in them 
a reduction of work and an earlier advance to the high 
school point. Thus those who are on their way to the 
college will lose no time; but they will have changed 
some of the needless repetitions or premature exactions 



Educational Progress in California. 13 

of the grammar years for the more careful and thorough 
studies of the high school. 

The State University has made good progress during 
this last decade, notwithstanding the difficulties as to 
preparation. Some academies and private schools have 
helped to fill the place of the missing high schools. 
Liberal aid has been given by the State to its University 
by a continuing tax. The staff of instruction has been 
much enlarged, with a corresponding expansion of the 
courses offered to the students. Special aid has come 
to the Agricultural and Mechanic Arts courses from 
a supplementary Morrill Aid Fund. The professional 
schools connected with the University have a much 
larger number on their rolls. Denominational colleges 
and schools have sprung up at various points in the 
State. 

So much for the history of this fourth decade. The 
fifth is but beginning. But 

VI. The new decade opens with extraordinary 
promise of educational development. Three things are 
especially worthy of note: 

1. The springing into life of a new and powerful 
university. I need not say where it is situated, nor 
what name it bears. The people of California have all 
heard of it, and have all been interested in its brilliant 
beginnings. To our educational force in this State an 
entire new Faculty has been added by the magic wand 
of wealth. This corps of able scholars and accom- 
plished teachers has become known already in all our 
educational circles. You welcome some of their num- 
ber at this meeting of the State Association. 

2. A second important event of the year 1891 is the 
movement for the University Extension. It is already 



14 Riverside Addresses. 

general, and promises to become almost overpowering. 
It is not endemic, but epidemic, affecting the whole 
country, and coming almost as swiftly as the grippe. 
Earlier and more slowly it grew up in Great Britain. 

But no such movement is capriciously causeless. In 
our own country there was a deliberate and widespread 
effort to popularize knowledge, through the Chautauqua 
movement. That movement reached a multitude of 
earnest minds, and has made itself felt in this State. 
When a higher plan came in, under the name of Uni- 
versity Extension, it found the public ready and eager 
to welcome it. 

Just what form University Extension is to take in 
California, it is too early to judge. If it can be kept 
on a true university level, it will do much to carrj^ the 
higher instruction to those who cannot attend college 
classes. In that case, it will call for a large increase 
of the University Faculties. The field work will rival 
in its demands the proper home work of the univer- 
sities. If too many places are clamorous for their share 
of attention, there will be encouragement for some 
adventurers, coming in by doubtful doors, who will not 
satisfy the more thoughtful minds. There are many 
problems still unsettled in the application of this sys- 
tem to our communities. But some form or forms of 
UniversityExtension will surely play a prominent part 
in California in this last decade of the nineteenth 
century. 

3. There is much more demand for distinctive courses 
of instruction in the interest of the teaching profession. 
Normal schools there have been for many 3^ears. Now 
there is a call for a similar and higher professional 
training in the Universities. Chairs of pedagogy have 
been established in manv institutions. Harvard has a 



Educational Progress m California. 15 

new Professor of the History and the Art of Teaching. 
Yale gives several courses in pedagog3^ The univer- 
sities of this State recognize this as an important 
department of instruction. 



This review of educational progress in California is 
necessarily very incomplete; but it shows that no cata- 
clysm has taken place in our educational histor^^ 
During all these decades there have been forces at 
work for the promotion of the educational interests of 
the State. If these interests are now prosperous, it is 
in sequence of previous long-continued and earnest 
efforts. If there is a harvest for the teachers of Cali- 
fornia to reap in the near future, it is because some 
patient husbandmen have sown the seed. 

We that are older almost envy the young teachers 
who are to take part in this new and larger progress. 
But there is a certain satisfaction in having helped to 
lay foundations. And let me utter a note of warning. 
If in these coming years the teachers lose their love 
for their work, if they forget the self-sacrifice which 
that work implies, and cease to emulate the single- 
hearted devotion of the pioneers, if the}^ seek rather 
for easy and comfortable places, then true educational 
progress will cease. Young ladies and gentlemen, you, 
too, must be pioneers for a still better and brighter 
future. You, too, must help to lay foundations which 
shall be out of sight and forgotten, it may be, that the 
future temple of education may rise, sacred and glorious, 
in this home of our love and our hopes. 



16 Riverside Addresses, 



THE SOCIAL SCIENCES AS AIDS IN TEACHING 
HISTORY. 



By Bkrnard Moses, 

Professor of History and Political Economy. 



During the few moments in which I may engage 
your attention, I shall invite you to consider the social 
sciences as aids in teaching history. A certain justifi- 
cation for bringing this matter before you may be found 
in the position which history and kindred subjects now 
occupy in the general scheme of academic studies. 
What this position is may be seen by glancing at the 
historical development of the curriculum. 

Considered with reference to its growth, the primary 
phase of the academic curriculum is that in which 
religion is the sole topic embraced. The Mohamme- 
dans, who found the Alexandrian library superfluous, 
in so far as its books agreed with the Koran, and use- 
less, in so far as they differed from it, were the products 
and the advocates of this simple curriculum. It 
appeared again in the Middle Ages, when the Christian 
church, in its pretensions to omniscience and absolute 
authority, essayed to fix the limits of human inquiry, 
Galileo might not teach that the earth moves, because 
this proposition was not in the predetermined circle of 
knowledge. 

The first considerable extension of the realm of 
knowledge was made through that great intellectual 



Social Sciences in TeacJiing History. 17 

movement which we call the revival of learning. This 
opened to modern minds a buried and almost for- 
gotten civilization, a civilization whose art and poetry 
and philosophy transcended the highest conceptions of 
those to whom it was revealed. The study of antiquity 
drew to itself a constantly increasing number of 
scholars, and, in their enthusiasm for ancient learning, 
all other subjects remained in comparative neglect. 
But on this study of ancient literature and ancient 
institutions, the church looked with suspicion. It 
feared the anti-christian influence of pagan thought. 
It feared a revival, not only of the learning, but also 
of the worship of .paganism. It feared the loss of 
stability and power in the presence of the unshackled 
mind, and, therefore, the means for developing the new 
learning had to grow up outside of the cloister and 
find other supporters than the clergy. The secular 
authorities in states and cities then became the patrons 
of learning and the founders of schools. The oldest 
universities of Italy and Germany were established 
under the impulse of this spirit; and thus the demand 
for instruction in the new field, which the church would 
not satisfy, was met by the wise liberality of princes 
acting in behalf of the states whose secular power 
they wielded. With the development of the new 
learning, theological teaching came out of the cloisters 
and was established at the universities. The church 
ceased to be the sole patron of education, and scholasti- 
cism no longer covered the whole field of thought and 
inquiry. A new topic was added to the curriculum of 
human knowledge. To the study of divinity was added 
the study of the humanities. 

Through the influence of the attractive revelations 
of antiquity and the powerful prejudice of the church, 
2 — A 



18 Riverside Addresses. 

the early discoveries in the realm of nature either 
suffered neglect or were regarded as unfit material for 
academic teaching. But in the first half of this centur^^ 
was revealed the second great intellectual revival of 
modern times. The fragmentar}^ and unsystematic 
investigations of earlier scientists grew into a system- 
atic and well-ordered search for scientific truth, and 
the results of this search, not less wonderful to the 
nineteenth century than were the revelations of the 
literary revival to the fifteenth, have grown into that 
body of knowledge which we call modern science ; and 
this science, opposed at first by the church and neg- 
lected by the humanists, now takes its place by the 
vside of scholasticism and the humanities in the great 
universities of the world, and forms a new addition to 
the field of learning. Thus to the primitive curriculum 
embracing the subjects properly involved in the study 
of religion, each of the ages in question has added a 
new topic or a new department of academic instruction. 
One has added the humanities; the other, modern 
science. 

In these last decades, a fourth topic, or department 
of study, has been added to the list, and it could not 
well have been added earlier. During the seventeenth 
century and the early part of the eighteenth, the 
period of European absolutism, when society was sup- 
posed to be directed arbitrarily by the capricious will 
of an absolute ruler, there was little incentive to study 
the history of society or to attempt to discover the laws 
of its activity and growth. But by degrees it came to 
be generall}^ acknowledged that the ultimate political 
power in the state, that power which is the source of 
all delegated authority, rests with the people. So long 
as the people had no share in the political control 



Social Sciences in TeacJiing History. 19 

of society, their knowledge or their ignorance of the 
principles and practices of public administration was a 
matter of little concern. There was no inducement for 
them to acquire knowledge of the details of govern- 
ments in which they had no voice ; but when the 
power to decide, either directly or indirectly, all ques- 
tions of public interest devolved upon the people, it 
became a matter of grave importance that they should 
be instructed in the history of society and in the laws 
and principles which underlie its organization, activity, 
and growth. There arose, therefore, a demand for an 
enlargement of the field of instruction, which should 
embrace especially the subjects of histor}^, economics, 
and politics ; and this group of subjects constitutes the 
latest important addition to the curriculum of academic 
studies. 

During the last forty }' ears this department of knowl- 
edge has become more and more important in the 
academic instruction in America, and the leading uni- 
versities have yielded to it a wider and still increasing 
place among the several courses of study. Many of 
us, still not very old men, remember distinctly the time 
when history was not considered of sufficient impor- 
tance in the curriculum to demand the exclusive atten- 
tion of an instructor. It was turned over somewhat 
indiscriminately to any member of the Faculty who 
might happen to have fewer and less exacting engage- 
ments than the others. It w^as not thought necessary 
to consider his attainments ; any one who could read 
and understand a plain narrative ought to be able to 
teach history. What changes the period of a genera- 
tion has wrought in the academic standing of these 
subjects may be seen by observing their present place 
in the curriculum of some of the leading universities 



20 Riverside Addresses. 

of this country : Harvard has forty courses taught by 
twelve instructors of different grades ; Yale thirty 
courses, with ten instructors ; Columbia thirty-one 
courses, with eleven instructors ; Cornell twenty- 
seven courses, with ten instructors ; University of 
Michigan thirty courses, with nine instructors ; Uni- 
versity of California twenty-two courses, with four 
instructors. 

An examination of these courses will reveal the fact 
that while the several studies of the group dealing with 
historical, economical, and political phenomena bear 
different names, they are all nevertheless designed to 
contribute to a common end, and that is to render a 
rational account of society. The whole group, as now 
constituted, is in some sense an outgrowth of the course 
of instruction in history as primarily organized. Its 
purpose is an enlargement of the purpose of instruction 
in history. As formerly presented, history showed us 
somewhat of the activity of a nation, but it left much 
to be known as to the nature and organization of the 
nation. To supplement the knowledge of society 
which history furnished, the science of economics was 
introduced, which undertook to give a scientific 
account of the industrial and commercial organization 
and activity of the nation; while a little later political 
science came to enlarge our knowledge of man's polit- 
ical relations and activities. 

All the subjects arranged in the curriculum under 
these three general heads of history, economics, and 
politics will be found, on thorough examination, to be 
closely united by lines of mutual dependence. History, 
as the comprehensive record of the internal affairs and 
foreign relations of nations, necessarily involves discus- 
sions of the subject-matter not only of economics, but 



Social Sciences in Teaching History. 21 

also of politics. The internal affairs considered are 
not simply those relating to distinguished persons, on 
whom has fallen by the accident of birth the nominal 
guidance of the public administration ; rather that 
part of internal or domestic history which relates to 
the industrial and commercial order and progress of a 
nation. The popular side of national life has become 
especially conspicuous during the present century, for 
two reasons: 

1 . Because of the unprecedented development of the 
commercial and industrial interests of society. 

2. Because of- the transfer of political power from 
an irresponsible head of the state to the bod}^ of the 
nation. 

These changes have turned attention to the people, 
and led the historian to emphasize especially popular 
interests and enterprises. These phases of national 
life have become so conspicuous that it has been found 
to be desirable to rewrite, from a new point of view, the 
history of certain nations, particularly those preeminent 
in industry and commerce. The history of England, 
therefore, in its latest version, under the hand of Mr. 
Green, becomes a "history of the English people." 
Another consequence of the conspicuous position to 
which the people have risen in this century is the 
development of studies in civilization, whether in the 
form of the German Cnltnrgeschichte, or the French 
and Enghsh history of civilization, or studies on the 
nature and progress of society. The internal history 
of any nation now demanded from the teacher is that 
which includes not only the phenomena of trade and 
industry, of mone}^ and taxation, but also the whole 
body of facts from the life of the people, which consti- 
tute the data of economics, the phenomena which it is 



22 Riverside Addresses. 

the business of economics to explain. In order, there- 
fore, to understand that part of a nation's history which 
is here referred to, one has need to know not merely the 
data of economics, but also the explanations of the data 
which the science of economics has to offer. To know 
histor}^, one must first know something of economics. 
To be an historian, one must first be something of an 
economist. 

In so far, moreover, as history sets forth foreign 
relations, it describes public activity in reference to 
that body of rules which are supposed to govern 
nations in their dealings with one another ; and in 
order to understand this activity, and to be in a posi- 
tion to speak with critical judgment upon it, which 
it is the business of the historian and the teacher of 
history to do, one must know this body of rules; in 
other words, one must have a sufficient knowledge of 
international law. 

The teacher who has read carefully in economics and 
international law will be in a condition to bring to his 
classes illustrations and explanations which hitherto 
have been generally wanting in the teaching of history, 
and because the}^ have been wanting students have 
regarded the subject as somewhat stale, flat, and un- 
profitable ; and in this matter the judgment of the 
students does not appear far from the truth. The 
histor>^ of the action of the French Revolutionary 
government regarding its revenues and expenditures, 
for example, has no interest, and appears to have little 
significance, except as we are able to bring to its con- 
sideration a knowledge of the economics of money and 
the fundamental principles of finance. In the histor}^ 
of this country, moreover, there are many phases which 
cannot be fully comprehended, except in the light of 



Social Sciences in Teaching History. 23 

economic principles ; and many controversies into 
which we have fallen with other nations cannot be 
adequately appreciated and correctly estimated, ex- 
cept we know the bearing of international law on 
the questions involved. 

But as an aid in understanding history, the science 
of politics is even more important than economics or 
international law. Dealing with the nature, functions, 
and structure of the state, it enables one to get clear 
and definite conceptions of the elements whose activit}^ 
constitutes the subject of the historical narrative or 
discussion. Unless we are able to assign a precise 
meaning to the various terms used relating to gov- 
ernment and societ3^, historical writing will neces- 
sarily appear vague, and the vagueness will either 
become wearisome and prevent long-continued read- 
ing, or will engender indifference to accuracy of 
thinking. But if we know that sovereignty means 
the power vested somewhere in the political organism, 
by which the fundamental positive law is issued and 
may be changed, and that the sovereign is the person 
or organized body of persons holding this power, we 
are in a position to appreciate the full significance of 
these terms when used correctly, and to detect the error 
when used incorrectly ; and b}^ thus alwa^^s moving in 
the light of a clear understanding, we may avoid con- 
fusion, and hope to reach the truth. On nearl}^ every 
page of history there is some record of the action of 
the state, and a large number of readers are in the 
absurd position of following the narrative of a course 
of activity, without having a clear and definite con- 
ception of the limits and qualities of the subject acting. 

And before the science of politics was developed for 
the enlightenment of the historian, his work showed a 



24 Riverside Addresses. 

tendency to become a royal chronicle amplified by 
voluminous details of military affairs. But scientific 
analysis of political phenomena has helped to clarify 
our views of society, and make history in this age more 
completely than ever before a comprehensive account 
of the progressive national life. It has revealed to us, 
moreover, the distinction between the state and the 
nation, showing the state not as a divine incompre- 
hensible something, but as that bod}^ of persons in the 
nation who have political rights, and are united in an 
organization to wield the power of the nation in behalf 
of the nation. The state, therefore, stands revealed 
by modern political science as a purely human institu- 
tion, which has come into its present complex form 
only gradually as the needs of public agencies to do 
the gradually increasing public work have appeared. 

Through the science of politics we are made to see 
not only what the state is, that is to say, what the 
organism is whose actions form a large part of the 
subject-matter of history, but also to see by what special 
agencies within the state the various departments of 
the public work of society are carried on. On this point 
the student in the early 3^ears of his study of history 
has much need of enlightenment ; for the historian, 
while treating of the progress effected by the public 
action which has been carried on through these agencies, 
often leaves us entirely uninformed as to the nature, 
structure, and relations among themselves of these 
agencies. Yet, under the present organization of 
instruction, students may not be expected to acquire 
this information before beginning the study of history, 
however necessary it may be to clearness and accuracy 
of historical knowledge. 

If, then, we conclude that much of the information 



Social Sciences in TeacJiing History. 25 

which is involved in the sciences of economics and 
politics is essential to an enlightened understanding of 
history, and that students cannot be required to make 
independent acquisitions in this line until late in their 
academic life, we are obliged to find means to remedy 
this defect and prevent their early-acquired historical 
knowledge from being vague and unprofitable ; and in 
this search we are turned to the method of teaching. 

In presenting a subject in history, no teacher in these 
days is likely to be satisfied to leave the topic with the 
meager statement of the text-book ; and he is, there- 
fore, compelled to devise some feasible means for ex- 
tending this information. In this matter he will be 
led to accept not necessarily the best means abstractly 
considered, but the most serviceable in view of the 
time and appliances at command. These usually reduce 
themselves to two. The first is to require the student 
to read indicated passages in various authors on the 
topics treated in the text. Given practically unlimited 
time, all the books desired, and a certain ripeness of 
the critical judgment, this method may be employed 
with great advantage. But these conditions are all 
wanting in the schools below the university, and even 
in the lower classes of the university itself. When- 
ever a large class is being taken over a given course of 
instruction, and all the members are reading the same 
list of indicated passages, they will meet with embar- 
rassment in any library in this country, on account of 
lack of books. This plan is, therefore, practicable only 
after the elementary stages of historical instruction have 
been passed, those stages in which the work of all the 
students is of necessity essentially the same. 

Even if these physical difficulties were removed, it 
would not be advisable to give this method more 



26 Riverside Addresses. 

tlian a limited application. In the early d.a3^s of the 
discovery of German universities by American students, 
the methods there employed made a profound impres- 
sion. The young men who came back to teach in 
American schools or colleges, were moved to give 
instruction by lectures. They forgot the conspicuous 
differences between their own positions and the posi- 
tion of the German professor. They forgot that the 
German students came to the lectures already possess- 
ing many of the attainments which belong to a liberal 
education, and that the professors had something to 
communicate not found in the ordinary text-book; 
often the results of their own investigations, which 
had not been embodied in the literature of the subject 
in hand. The professor of the German university 
spoke to 3^oung men already familiar with the elements 
and outlines of the sciences, and who wished to learn 
the sources of further information. Pointing out and 
criticising these sources was often a large part of the 
lecturer's work. These conditions were all wanting, 
and are still wanting, in a large part of the field of 
academic instruction in this country; and the German 
method of lecturing, apart from its proper conditions, 
was absurd. It had an application and was the only 
practicable method in the early history of education, 
when books were few and inaccessible to most learners. 
Again, in these times, when books have become bewil- 
deringh^ abundant, the academic lecture, in so far as it 
is a giving of special methods of investigation and 
criticism of sources, has become useful for students of 
large attainments. These conditions may be found in 
the graduate department of our universities, and per- 
haps to a certain extent in the highest grades of the 
undero:raduate courses. 



A^^^^OMS^^ 

Social Sciences in TeacJmtg History. 

In these last years, moreover,' the Am.enca,ii teacher 
has discovered the seminar}- niethod. 'iTiiis' wass^al^ 
brought to light in Germany. Tn^^d^ii bl irt$ji:«c!ion 
which it involves has numerous excellences, but it is 
not adapted to all circumstances. It is undoubtedl}^ a 
proper auxiliary in the highest grades of instruction 
where students under competent direction are pursu- 
ing independent lines of research. But its extensive 
employment in the early years of historical study is 
questionable. Specialized investigations in history 
from the beginning of the student's career lead to the 
danger of knowing everything without knowing the 
whole. The knowledge of the facts relating to any 
particular event, unsupported by a synthetic under- 
standing of the whole course of human experience, and 
by an appreciation of the historic place of this event, 
is scarcely more important than a knowledge of the 
fictitious events and characters of Scott or Balzac. 
History as an academic study means more than this; 
and, to make it more, some plan of study must be 
had which shall defer the minute investigation of 
special points till the mind has been trained to grasp 
as a unit the whole record of progressive societ3^ If 
one would be an historian, or merit mastership in this 
department of knowledge, it must become habitual for 
him to view events in the large. To this end, the 
scheme of western history should be unfolded before 
him at the beginning of his studies, and kept before 
him through all his subsequent work. At first, a mere 
skeleton in his mind, from year to 3-ear it acquires a 
greater and greater fullness of detail, until at last he 
finds himself in possession of a comprehensive and 
well-balanced general knowledge of histor3\ At this 
point some limited field may be selected, and made the 



28 Riverside Addresses. 

object of his special inquiries. To this lie may then 
direct whatever force and scholarly insight he can com- 
mand, and not be in danger of failing to appreciate the 
proper relation of his special subject to the whole of 
which it is a part. But to direct the immature student 
to the study of special points in history is to cause him 
to become habituated to small views, and to render him 
liable to be hopelessly lost in details. He may know 
the record of certain events, but never rise to the larger 
conception of history. 

The second plan for extending the range of the stu- 
dent's information is that under which the teacher fur- 
nishes a more or less elaborate commentary on the points 
involved in the text. In carrying out this plan, an item 
of first importance is to determine what books shall be 
used by the students. An objection is raised against 
the use of the ordinary text-book, on the ground that 
it is meager and lifeless, and that supplementary read- 
ing cannot be done by a large class with advantage. If 
there were no physical difficulties in the way, students 
would be likely to read extensively on some points, and 
only a little on other points, perhaps more important, 
according to the facility of obtaining the literature 
desired. Both of these difficulties ma}^ be avoided by 
putting into the hands of each student a book by a 
recognized master of the subject to be considered, and 
not by a mere text-book maker, which shall contain all 
that we may require the student to read, even when 
under the highest pressure. If, to illustrate by a single 
example, the subject for the term in the university is 
English history in the eighteenth century, let each 
student have the eight volumes of Lecky's " History of 
England in the Eighteenth Century." The advantages 
of this over the small text-book and outside reading 



Social Sciences in Teaching History. 29 

are numerous. In the first place, what the student 
reads on the subject will be in proportion to the impor- 
tance of the several parts of it, since he will take it in 
the form in which a great historian has viewed it and 
set it forth. He will, moreover, have all the material 
of his work at hand for reference at all times. He will 
learn to read a voluminous book, which is a matter of 
vast importance for the youth who would be a student ; 
and after a few undertakings of this kind, he will not 
be deterred from seeking information because it happens 
to be contained in a work of several volumes. The diffi- 
culties which arise from attempts to supplement the 
deficiencies of the small text-book do not appear here ; 
and if the opposite ma}^ sometimes hold, the teacher 
may use his discretion in directing limitations, and no 
embarrassment will ensue. With such a text before 
the student, the teacher will not be tempted to waste 
time in giving, by way of informal lectures, what can 
be much better acquired from the book itself. Never- 
theless there should be comment, but the nature of it 
will depend very largely on the character of the book 
used ; but in general it ma}^ be said that the teacher 
should illustrate by setting forth the principles of social 
order and progress, rather than consume the time in 
elaborating the narrative. Merely extending the story 
of historical events adds very little to our understand- 
ing of the subject ; but analysis of the state and society 
reveals to us the mode of organization, the instrumen- 
talities of social action, and the forces by which the 
nation is moved along the course of improvement. 

But this involves on the part of the teacher certain 
attainments in economics and political science, and it is 
the importance of these attainments for the teacher of, 
history that I wish to emphasize. The special char- 



80 Riverside Addresses. 

acter wliich historical studies will assume under differ- 
ent circumstances will depend very much on the kind 
of opportunities which these different circumstances 
present. In European countries where the scholar has 
access to the sources of historj^, whether in great libra- 
ries or in the archives, his investigations are likely to 
be largely directed to setting forth hitherto unknown 
details. But in a country like this, whose civilization 
is but of yesterday, and which has no sources except 
for the history of a few recent generations, historical 
study will necessarily be turned to some other end. 
The American scholar is unable to compete success- 
fully with the European scholar in searching out the 
details of early European history; and his energy and 
taste for social studies will tend, therefore, to find satis- 
faction in the scientific interpretation of the historical 
facts presented by European historians, and in the 
development of those social sciences which take their 
data from history. 

But hitherto the achievements of this nation on any 
of these lines have not been remarkable, yet this fact 
does not indicate a lack of worthy political thought. 
In the field of political theory, Roman literature, to 
illustrate, is specially barren, yet no one will deny that 
the Romans thought much and well on political prob- 
lems. Their thinking was given expression and form 
in laws and practical institutions rather than in treat- 
ises; and in this regard the people of the United States 
are comparable with the Romans. For more than a 
hundred years this nation has been deeply absorbed in 
the work of building a great state; and the best the 
nation has thought has been embodied in the institu- 
tions and laws, giving them in some sense the char- 
acter of original creations. But the large place occupied 



Social Sciences in TeacJnng History. 31 

by social subjects in the universities, and the large 
number of men giving to these subjects their thought- 
ful attention, are conditions speciall}^ favorable to the 
production of an important economic and political 
literature. Here the parallel with Rome ends. While 
the Roman republic fell under imperial rule which 
choked all political discussion, this republic has entered 
upon that phase of its history in which thoughtful 
political discussion has become a necessary condition of 
continued healthy existence. And the present activity 
in the study of society suggests that the nation ma}^ yet 
make achievements in economics and political science 
worth}^ of the originality already displayed in practical 
politics. 

There are good reasons why some part in cultivating 
this field should fall to the teachers of histor}^, not 
merely in the universities but also in the other schools 
throughout the countr}^ The first of these is the gen- 
eral fact that independent work, which results in an 
advancement of knowledge, is essential to the highest 
efficiency of the teacher. The teacher who ceases to 
be an investigator, who ceases to seek to enlarge his 
mental vision by scholarl}^ inquiries, is in danger of 
stagnation and the consequent loss of the reasonable 
ground of his calling. Another circumstance by which 
the already mentioned line of study is commended 
as a proper field for the teacher's independent inquiries, 
is the fact that, while in the realm of pure historical 
research adequate sources of information are found in 
only a few places, in the auxiliary subjects of economics 
and political science one may alwa3"S have at hand 
abundant material for original work. There are always 
within his horizon the data of some hitherto unsolved 
social problem. The society in which he lives is the 



32 Riverside Addresses. 

laboratory in which experiments are constantly going 
on before his eyes. 

The analysis of social institutions, moreover, will 
faciHtate an understanding of that peculiar and distinct- 
ive characteristic of western society which we call 
progress, and thus throw a light on history that cannot 
be derived from any other source. In this light one 
may see clearly the unsoundness of the favorite expres- 
sion of the half-instructed, that history repeats itself. 
With our knowledge of history, enlightened by an 
understanding of the structure and moving forces of 
society, it becomes evident that that movement which 
is observed in progressive society is never in a circle, 
but always on to new ground, though not always in 
an unswerving line forward. Progress is not contin- 
uous, nor always at the same rate; there are periods of 
halting, and even of retrogression, when deterioration 
marks many of the phases of life, when a mortal disease 
appears to have smitten a whole civilization. It per- 
ishes like the seed that is sown, but after the destruc- 
tion there rises a new and more fruitful life. The 
growth of society is, moreover, like the growth of a 
great city; built up little by little, it serves the pur- 
poses of a generation, but at last fails to meet the new 
needs. One by one its buildings are replaced by others 
of better plan and sounder make. Thus in social 
growth, old institutions that have fulfilled their mis- 
sion yield in time to institutions suited to the new 
wants of a more advanced society. A great revolution- 
ary movement sometimes sweeps the institutions of a 
nation to destruction in a day, as a fire sweeps away 
the various structures that have served the diverse 
purposes of civilized existence. Then the work of 
construction is rapid and free; and as the new city is 



Social Sciences in Teaching History. 33 

better than the old, so are the new institutions adapted 
to a higher and better social existence. But the old 
structures are never rebuilt, nor the old institutions 
recalled into active force. 

This general truth finds another expression in the 
statement of the fact that the practical social problems 
of no two ages are ever exactly the same. If the ages 
are far apart, all the conditions, even the nature of the 
persons involved, may be different. The men of this 
age, for example, who know from observation the 
marvels of modern life, have, as the creatures of other 
circumstances and other traditions, a nature different 
from that of the men who lived the narrow human 
existence of the Middle Ages. They are distinguished 
by a wider range of intellectual vision, a more compre- 
hensive grasp of the imagination, and a series of new 
impulses. Moreover, the physical conditions of to-day 
are utterly at variance with those of earlier centuries; 
and these two facts alone are adequate to make the 
social problems which we have to solve new problems. 
Because the problems of each age are new, social 
advancement can be achieved only by slow and costly 
experiments. The general place of experiment in the 
progress of society the teacher of history should under- 
stand, and for enlightenment he must turn to those 
writers whose business it is to analyze society and to 
set forth the laws of social order and growth. 

The fact that some points are still in debate in the 
sciences which deal with the phenomena of society, is 
not an argument against their utility as subjects of 
stud3^ Every science has a margin of unsettled ques- 
tions. These constitute the principal attraction for the 
independent investigator, and furnish him an oppor- 
tunity to make a permanent contribution to human 

3— A 



34 Riverside Addresses. 

knowledge. The comparatively late development of 
the social sciences is not wholly due to the influence 
of absolute government practicall}^ prohibiting the 
discussion of questions relating to political affairs, but 
also in part to the complexity of the data involved. 
The attempts to render a scientific account of society 
have made unusually prominent certain social phe- 
nomena, which, since they have been made specially 
conspicuous, the teacher of history is bound to consider. 
Even if he would, he may not present history as a 
chronicle of the achievements of the distinguished head 
of the state. He must set it forth in its character as 
the record of the most complex of organisms; and to 
learn this character there is no better source than the 
writings of those by whom this complexity has been 
specially revealed, and through whom a certain degree 
of scientific order has been brought out of the chaos of 
social phenomena. 

But political science has encountered even more 
hinderances than economics. The claims of monarch- 
ical rulers to hold a power of divine origin, and to 
be free from responsibility to the governed, made the 
theory of politics in some sense an appendage of theol- 
ogy. From the conception of the monarch as the agent 
of God, and of his power as the supreme power in the 
state, the step was easy to the conclusion that the state 
itself was divine. Metaphysics applied to politics be- 
came sterile and unprofitable. The only possibility of 
progress lay in taking a new point of view and a new 
method. This was not readily accomplished, for men 
hesitated to encounter the thunders of the metaphysical 
theologians, or the theological metaphysicians, which 
would necessarily follow the declaration that their 
whole philosophy of the state was unreal and empty. 



Social Sciences in Teaching History. 35 

Nevertheless, the interests of progressive knowledge 
demanded that the assumptions of metaph3^sical politics 
should be abandoned, and a new start made from ob- 
served and known data. With this beginning, and 
using the methods of ordinary scientific research, im- 
portant steps have already been taken toward the 
creation of a science of politics that will explain the 
phenomena of which it treats. And it is to this, and 
not to the theologico-metaphysical politics, that the 
teacher must look for light on the political and consti- 
tutional phases of history. 

An important function of the teacher of history, 
therefore, under the method suggested for work below 
the highest, is that of a judicious commentator on the 
topics involved in the student's reading, and in making 
these comments no information wall serve his purposes 
better than that drawn from economic and political 
science, in which are set forth the laws of social organ- 
ization as well as the forces and methods of progress. 



36 Riverside Addresses, 



THE PAST AND PRESENT OP ELEMENTARY 
MATHEMATICS. 



By Irving Stringham, 

Professor of Mathematics. 



In the long history of the world's intellectual progress 
nothing is more striking than the dependence of each 
succeeding age upon its predecessors for the materials 
out of which its own achievements are wrought. The 
raw materials we use in the manufacture of science are 
seldom dug up fresh from the earth, but are picked up 
by the wayside, where they were dropped by our prede- 
cessors, who could devise no use for them. It thus 
happens that the discoveries of Newton are old hints 
wrought over and made into the finished product of 
science by the master-mind, some of them dating back- 
wards nineteen centuries, to the time of Archimedes. 
The most transcendant genius works under limitations, 
cannot see far into the future; and if, by a fortuitous 
inspiration he anticipates a discovery that, standing out 
of relation to the knowledge of his own time, belongs 
to a succeeding age, it remains unused, unfruitful, and 
of no current value till such time as it can be correlated 
with other scientific knowledge. 

And so every science has a prehistoric stage, in 
which principles prospectively important are. at first 
merely the incidents in apparentl}^ unrelated problems 
or investigations, their first users perhaps entirely 
unknown and never to be identified. Only later, 



k 



Elementary Mathematics. 37 

possibly after repeated recurrence in investigations of 
which it is the true foundation, does the principle call 
attention to itself as of great importance. It is the 
recognition of its importance, not its first merely inci- 
dental use, that constitutes real discovery. 

The prehistoric period of mathematics belongs to the 
centuries immediately preceding the earHest develop- 
ment of Greek philosophy, and appears to have been 
first cultivated in connection with land surveying and 
astronomy in Egypt and Assyria. It had its begin- 
nings as a science in the latter part of the seventh 
century, B. C, at Miletus, where the Greek philosopher 
Thales, who had traveled extensively in foreign coun- 
tries and had resided for a time in Egypt, first taught 
geometry deductively; but nearly contemporaneously 
also at Crotona, where Pythagoras first established the 
principles of the doctrine of proportion, and laid the 
foundations of a goodly part of elementary geometry. 
Thenceforward, so long as Greek civilization existed 
anywhere, the study of geometry never ceased to be an 
important factor in the world's intellectual progress, 
and for more than twelve centuries the continuity of 
its study was unbroken. First, Thales at Miletus, 
then Pythagoras at Crotona, then Hippocrates at 
Athens, then Euclid at Alexandria, then Archimedes 
at Syracuse, then ApoUonius at Perga, then Pappus at 
Alexandria, wrought out in succession, classified and 
organized into scientific unity the great mass of propo- 
sitions which constitute the subject-matter of geomet- 
rical study in our schools to-day. 

Near the close of the Greek period, during which 
geometry, from the merest beginnings, had grown into 
a comprehensive system, the first published accounts 
of an algebraic analysis appear, the Arithmetica of 



38 Riverside Addresses. 

Diophantos, the last contribution of the great Alexan- 
drian school to mathematical science. This work, 
remarkable for its achievement of results, but lament- 
ably defective in method and organic unity, had in 
it the foreshadowings of a new science, but was in no 
respect the science itself It possessed no power of 
further growth from within, and when algebra finally 
became scientific it was constructed on entirely new 
models. 

But even if the work of Diophantos had been con- 
structed upon correct scientific principles, it would still 
have passed speedily into oblivion, for the light of 
Greek civilization was already feeble and flickering 
and was soon completely extinguished by the fanati- 
cism and bigotry that for seven centuries enveloped 
Europe in almost total darkness. In fact, the work of 
Diophantos was not rediscovered in Europe until the 
middle of the sixteenth century. 

With the disappearance of the Greek schools there 
seemed to be no hope for the further cultivation of 
mathematics as a science on the face of the earth, for 
nowhere else in the ancient world, up to that time, had 
any results of a high order been achieved. But at this 
critical juncture a new light appears for us in the east. 
The Arithmetica of Diophantos had been published 
(conjecturally) in the fourth century of our era, and the 
Alexandrian school continued in existence until the 
Mohammedan conquest in 641 A. D., during which 
time mathematics was still cultivated, though feebly, 
in the form of commentary or perfunctory study, and 
without originality or fruitful result ; and it was more 
than a centurj^ and a half before the final catastrophe — 
the capture of Alexandria and the burning of the great 
library by the Mohammedans — that there appeared in 



Elementary Mathematics. 39 

India a work on algebra and trigonometry by the 
astronomer Aryabhatta, of which no Greek mathema- 
tician of the earlier centuries would have been capable. 
From this time until the revival of learning in western 
Europe the Indians are the true discoverers in mathe- 
matical science. To what extent they were indebted 
to the Greeks for the raw materials out of which they 
constructed their algebra is not known, nor is it of 
consequence, for since the Greeks never succeeded in 
constructing an organic system of algebra, the indebt- 
edness could, in any event, have been but small. 

To the Indians, then, is due the credit of first creating 
algebra as a science. Two great works on mathematics 
and astronomy attest this claim ; one by Brahmagupta, 
written in 628, which expounds a complete system of 
algebraic analysis, the other by Bhaskara, in 1 1 50, upon 
arithmetic and algebra, in which the Indian system of 
arithmetic — the one we ourselves use — is employed. 
These works, however, record the highest achievements 
of the Indians in mathematics, and all subsequent prog- 
ress in algebra has taken place in the west, and in 
modern times. 

Though the Indians had shown themselves to be 
consummate algebraists, they were in no sense geome- 
ters; and far from adding any new thought to the sci- 
ence which the Greeks had created, they apprehended 
with difficulty and with much blundering what of geom- 
etry they received from Greek sources. Thus two great 
civilizations had stood on either side of a barrier which 
neither could pass. The Greeks had created geometr}-, 
but they could not invent algebra; the Indians invented 
algebra, but they could not add one proposition of im- 
portance to geometry. 

Out of these two independent sources issued the two 



40 Riverside Addresses, 

distinct streams of mathematical thought that flowed 
first sluggishly through the Mohammedan countries of 
Arabia, Africa, and Spain, thence finally into Christian 
Europe, where they were subsequently joined together. 
For it was from the Arabs that mediaeval Europe first 
acquired in the twelfth century some knowledge of both 
algebra and geometry. The Arabs, however, were not 
good conservers, or compilers, of the scientific knowl- 
edge accessible to them from Greek and Indian sources, 
and transmitted it in such imperfect form that many 
important principles had either to be rediscovered, or 
sought for in the Greek or Sanskrit, before Europe 
acquired full possession of the mathematical knowl- 
edge which Greece on the one hand and India on the 
other had contained. But be this as it may, Europe 
rapidly recovered, during the four centuries from the 
twelfth to the sixteenth, substantially all the mathe- 
matical knowledge that the ancient civilizations had 
bequeathed to their successors. 

During the sixteenth century mathematics received 
its share of that activity in intellectual pursuits which 
has received the name of the Renaissance; but its 
development was strictly upon the lines that had been 
marked out for it in ancient times. Geometry did not 
free itself from the limitations as to method and scope 
that had been set for it by Euclid, Archimedes, and 
Apollonius. Algebra followed the Indian model, which 
had been recovered with much difficulty by the help of 
the Arabs, and, barring a few geometrical constructions 
of algebraic equations, mere translations into modern 
forms of expression of well-known Greek demonstra- 
tions, did not get beyond the limited definition of 
algebraic quantity as rational or commensurable num- 
ber. Algebra and geometry were still two distinct 



Elementary Mathematics. 41 

sciences, and there were no indications, except in a few 
special instances, that the one was in any way suscepti- 
ble of interpretation in terms of the other. 

In the seventeenth century, however, three important 
steps were taken tow^ards a recognition of the intimate 
relations that we now know these two main divisions 
of elementary mathematics bear to each other, and 
which play such an important part in all modern math- 
ematical investigations. The first was through the 
invention of logarithms, in 1 614, by Napier; the second 
through the invention of analytic geometry, in 1637, 
by Descartes; the third through the invention of the 
differential calculus, in 1665, by Newton. 

The introduction of logarithms, however, important 
as it was as an essential part of the new analysis soon 
to be created, was recognized at this time only as sim- 
plifying the processes of arithmetical calculation. 

Both the analytic geometry and the differential cal- 
culus seemed to be necessary prerequisites for a full 
understanding of logarithms as a part of analysis, and 
a century passed before their importance as such was 
recognized; furnishing, in fact, a remarkable instance 
of a premature discovery. The ability to recognize the 
true import of the logarithm was made possible only by 
discoveries that came half a century after the logarithm 
itself had been invented. 

The discovery made known to the world by Des- 
cartes, in 1637, may be summed up in the words: Every 
function has a graph. To illustrate by a very simple 
example, the function x'^ has for its graph a parabola 
with its principal vertex at the origin of coordinates, 
and its principal diameter coincident with the /-axis. 
Thus: 



42 



Riverside Addresses. 



The values of x are represented by lines drawn hori- 
zontally from the origin O, to the left or right, from the 
extremities of which lines are drawn upwards to repre- 
sent the values of x^. Each pair of lines thus deter- 
mined by a pair of values x^ x\ fixes a point in the 
plane, and the aggregate of all such points range them- 
selves along the curve known as the parabola. The 
second quantity ^^, it is now customary to represent by 
a second letter, as j/, and to speak of x and y as func- 
tions of each other. In a similar manner any algebraic 
equation between two quantities, x andj/, has its graph. 

Now mark the radical departure here taken in the 
interpretation of algebraic quantities. A straight line 
stands as the representative of any such quantity, an 
interpretation wholly repugnant to Greek geometry. 
So long as his practice conformed to the canon which, 
from time immemorial, had been his guide in the geo- 
metrical interpretation of quantity, x^ could mean for 
the Greek only a square, an area, never a straight 
line. But his orthodoxy was the barrier to his further 
progress, and from the abandonment of that orthodoxy 
the modern mathematician dates the possibility of 
achievement beyond the limits of investigation which 
the Greeks had set for themselves. Henceforth, more- 



Elementary Mathematics. 43 

over, the interests of algebra and geometry were one 
and the same; progress in the one was to mean a simul- 
taneous progress in the other. 

Twenty-eight years pass, and we stand at the thresh- 
old of the greatest of the discoveries in mathematics 
of modern times — that of the differential calculus. The 
year is 1665, when Sir Isaac Newton communicated to 
some of his friends the fundamental ideas of the new 
method. 

Taken in connection with the new interpretation of 
the algebraic equation by Descartes, the scope of this 
method was so great as eventuall}^ — that is, within 
another century at most — to reconstitute the entire 
body of mathematical science upon a new basis, and 
to completely change the attitude of mathematicians 
towards the problem of its further advancement. 
Henceforth its various parts are not looked upon as 
disassociated systems having no common meeting 
ground, but geometry, algebra, trigonometr}^, analytic 
geometry, the differential and integral calculus, are 
seen to constitute one organic whole, or rather one 
organic unit in a much larger whole. Henceforth 
mathematics thus newly constituted is to have its 
alphabet, its nomenclature, its language, and whoever 
would use it for any purpose must learn its nomencla- 
ture and speak its language. Henceforth it is not to 
be the plaything of the philosopher, nor the recreative 
and disciplinary study of the scholiast, but the instru- 
ment of research and of efficient accomplishment of 
practical ends in the hands of the astronomer, the phys- 
icist, and the engineer. Such was the unparalleled 
achievement of the seventeenth century. 

But I must be more explicit. I am endeavoring to 
trace out, in brief outline, from the earliest times to the 



44 Riverside Addresses, 

present day, the development of the foundation prin- 
ciples of the two great divisions of elementary mathe- 
matics, geometry and algebra (but in particular and 
chiefly the latter), and that which concerns us primarily 
in the work of Newton is his introduction of the con- 
tinuous variable as one of the elements of algebraic 
analysis. For our present purpose it will be sufficient 
to describe the continuous variable as a straight line, 
having one of its extremities fixed at a point O, while 
the point P, which marks the other extremity, is free to 

O P 



move forwards or backwards in a straight line. When 
P moves without interruption in its path the variable 
quantity OP is said to change continuously, and is 
called a continuous variable. It may or may not be 
possible to represent it b}^ a rational, that is, a com- 
mensurable number. 

At last the materials for a complete grounding of 
algebraic science, in logicallj'' fundamental principles, 
were at hand. Napier had given us logarithms, Des- 
cartes had put into our hands adequate means for the 
graphical representation and interpretation of the alge- 
braic function, Newton had shown us how algebraic 
quantity could be freed from the limitation by which 
its meaning had always been confined to rational 
number. The materials for the work were indeed 
at hand, but they were in great part raw materials^ 
and the energies of mathematicians were expended 
upon testing and reshaping the powerful instruments 
of analysis just discovered and enlarging the scope of 
their application, and little attention was given to a 
reexamination of the foundations of algebra. Yet, as a 
science, founded upon logically scientific principles, 



Elementary Mathematics. 45 

algebra was still in the formative stage and required 
this reexamination in the light of the new discoveries. 
Two centuries have been just sufi&cient to accomplish 
the task. 

During the eighteenth century no important result 
was attained. The old algebra had acquired, during 
the centuries since the revival of learning, a momen- 
tum sufficient to carry its development forward upon 
the lines that had been originally set. But at the 
beginning of the present century a distinct step in 
advance was taken, by Argand and Gauss, through the 
introduction of the so-called imaginary as a quantity, 
having equal importance in algebra with so-called real 
quantity, and being susceptible of real geometrical 
interpretation. This step made it possible, as soon as 
its importance was fully understood, to define algebra 
for the first time. 

When a series of elements operating upon each 
other in accordance with fixed laws produce only other 
elements belonging to the same series, they are said 
to constitute a group. Thus all positive integers, sub- 
jected only to the processes of addition and multipli- 
cation, produce only positive integers, and hence form 
a group. 

The effect of introducing into the arithmetic of posi- 
tive integers the further processes of subtraction and 
division is to break the integrity of the old group and 
form a new one whose elements include, not only posi- 
tive integers, but all rational numbers, both positive 
and negative, integral and fractional. A final step 
through involution, or the extracting of roots, with its 
allied processes, leads in a similar way to imaginary 
and complex numbers— that is, numbers composed of 
both a real and an imaginary part. 



46 Riverside Addresses. 

Now if, as is legitimate, we regard all reals and imag- 
inaries as special forms of complex quantities — reals 
having zero imaginary parts, imaginaries having zero 
real parts — then the algebraic processes of addition, 
subtraction, multiplication, division, evolution, involu- 
tion, and the taking of logarithms, applied to complex 
quantities in any of their several forms, produce only 
other complex quantities. And hence: 

The aggregate ^of all complex quantities — includ- 
ing all reals and imaginaries^ both rational and 
irrational — operating upon each other in all possible 
ways by the i^ules of algebra, form a closed group. 

If, in an algebra the elements that constitute the 
subjects of its operations form a closed group when 
subjected to a complete cycle of such operations, such 
an algebra may be said to be logically complete. 

Now, in the elementary algebra we teach in the 
public school, involution and the logarithmic process 
form an essential part, and through them imaginary 
and complex quantities make their appearance as un- 
avoidable subjects of its operations. They are neces- 
sarily elements coordinate with the real quantities of 
our algebra, which is therefore logically, and as we 
now agree, also practically, only the fraction of an 
algebra, if the complex quantity be left out of it. The 
inability of the earlier algebraists to recognize this 
fact made it also impossible for them to carry out the 
algebraic processes of involution and the taking of 
logarithms to any except real and positive numbers. 

l^et us glance, for a moment, at what was further 
necessary in order to complete the foundations of our 
mathematical superstructure. The early works upon 
arithmetic and algebra had been little more than mere 
collections of rules for the solution of problems. Few 



I 



Elementary Mathematics. 47 

principles were explained, none adequately, and this 
feature of logical incompleteness has remained promi- 
nent, with rare exceptions, in all text-books upon 
algebra up to the present time. By tradition, algebra 
became a mere mechanical device for turning out prac- 
tical results, by careless reasoning errors crept into the 
explanation of its principles, and through incompetent 
compilers were perpetuated in the form of current liter- 
ature, and thus, instead of becoming a classic like the 
geometry handed down to us from the Greeks in the 
form of Euclid's elements, algebra became a collection 
of processes practically exemplified and of principles 
inadequately explained. 

The binomial theorem was either assumed to be true 
for negative and fractional indices by mere analogy 
from one or two special cases, or a logically unsound 
proof was adduced and actually remains in nearly all 
of our text-books to-day. No attempt at all was made 
to justify the associative, commutative, and distributive 
laws in the four fundamental processes. 

Hence the necessity of a thorough overhauling of our 
algebraic sj^stem at the beginning of the nineteenth 
century. We have now accomplished the task; how 
well, posterity will decide. Abel, in 1829, examined 
thoroughly and laid down once for all time the con- 
ditions under which development by the binomial 
theorem is possible: and in 1870-71 Weierstrass and 
G. Kantor gave us a new definition of irrational num- 
ber, and established the doctrine of the irrational upon 
a strictly logical basis; and at about the same time 
(1870), Benjamin Peirce produced the final scientific 
formula into which our present definition of algebra is 
cast. It would take me too far afield to go over these 
matters here in detail. They require, in fact, days, 



48 Riverside Addresses. 

rather than hours, of careful study for an adequate 
understanding of them, and I must content myself 
with referring you to the literature upon this part of 
the subject under discussion, which is now in exist- 
ence and easily accessible. 

The hurried survey we have now made of the course 
which mathematical thought has taken within the two 
great divisions of its work since the earliest times, 
shows how at every step in the progress of mathe- 
matical science, whether in the domain of algebra or 
geometry, it has seemed impossible for the mind to free 
itself from the tendencies, or avoid following out the 
line of development, which some previous age or gen- 
eration has predetermined for it. Slow indeed has been 
our progress, if we merely count the centuries through 
which the struggle against difficulties has been main- 
tained, though the achievement has undoubtedly been 
very great. 

But standing, as we do now, near the close of the 
twenty-fifth century since mathematics became a 
science, and taking advantage of the discoveries of 
our predecessors, we may pass across the entire field 
that outlines the foundations of algebraic science, and 
seizing only upon those principles that mark its epochs 
of advance and are cardinal, construct an algebraic 
system which shall have all the logical rigor and com- 
pleteness of Greek geometry; and for the accomplish- 
ment of this task no serious difficulty longer stands in 
our way. The materials are at hand for the purpose; 
it only requires some master's hand to mold them into 
coherence. 

lyCt me indicate, in the briefest possible way, what 
the cardinal principles referred to are, and how they 
constitute the foundations of algebra. They are the 
following: 



Elementary MatJiematics. 49 

1. The doctrine of proportion, first formulated by 
Pythagoras (560 B. C), but systematized and com- 
pleted by Euclid (300 B.C.). This includes the theory 
of the irrational, and leads directly to the definitions 
of multiplication and division in algebra. 

2. The introduction of general principles or rules for 
the fundamental processes of arithmetic and algebra, 
by the Indians in the early centuries of the Christian 
era. 

3. The introduction of letters and symbols of oper- 
ation, such as -[-, — , X, ^, =, log., exponents, etc. 
This has been done gradually, by many hands. 

4. The invention of logarithms, by Napier (16 14), 
out of which the law of indices (exponents) also pro- 
ceeds. 

5. The graphic representation of algebraic functions 
(by curves), by Descartes (1637). 

6. The introduction of the continuous variable, by 
Newton (1665). 

7. The introduction and graphic representation of 
imaginary quantities, by Argand (1806). 

8. The final definition of algebra, due to the general 
reconstruction of algebra during the nineteenth century, 
by Grassmann, Cayley, Sylvester, Peirce (1845-1870). 

To fill in this outline would be the writing of a book. 
Two demonstrations must serve the purpose of giving 
you a hint of the mode of procedure. They shall be 
the answers to the two questions: 

{a) How is the definition of multiplication derived 
from the theory of proportion? 

(b) How, by proper definition and by the help of the 
graphic method and the continuous variable, can we 
prove the law of indices (exponents)? 

(a) Multiplication. — The propositions of proportion 
4— A 




50 Riverside Addresses. 

are assumed to be true, as proved by Euclid, not by the 
algebraic method used in American text-books. Let 
a and b be any two magnitudes laid off upon two 
straight lines, making any convenient angle with each 
other. At O lay off OB=(^, OA=^, and on OA, in the 
same direction as OA, lay off OJ, which shall be of 
fixed length in all constructions belonging to algebra, 
and shall be called the unit. Join J and B, and draw 
from A a straight line parallel to JB to intersect OB 
in M. 

Then, by the theory 
of proportion in the 
similar triangles OJB, 
OAM, 

j\b\ \a\ m . [/;^:=0M] . 
The line-segment 
OM=;;2 is defined as the algebraic product of a by b^ 
and is denoted by (^X<^.* 

The law of commutation, namely: a^b=by^a, fol- 
lows at once from Euclid, V. i6, which proves that if 
j\b'. \a\in 
.'. j:a\ :b:m, 
of which proportions the first states by our definition 
that 

m^=aXb; 
the second that 

7u=bX(^' 
If 7n be equal to j, then 

j:b: \a\j 
and b^ a are called the reciprocals of a^ b^ respectively; 
and they are written thus: 

y/(^=reciprocal of a^ 
j I <5=reciprocal of b^ etc. 

* Descartes, la Geometrie (1637), reprint of 1886, p. 2. 



Elementary Mathematics, 51 

If (^=y in the proportiony:*^: \a\m^ then 

j\b\ 'J'.m^ that is m^=b; 

but by definition m=j X b 

.-. jXb=b 
and in particular 

which is the well-known property of unity. 
Again, the proportion^* : '-'.(^'J defines 

b=j la, a=jlb, ayib=j -, 
hence, 

a X b=a Xj / ^=J X ^ / ^=<^ / ^^Z, 

and similarly 

bxa=b/b=j. 
Also, 

aXj/b=jX^/b=--a/b. 

Thus ^/<^ is a fraction or quotient in the algebraic 
sense. 

These examples suffice, no doubt, to convince you 
that all the laws of algebraic multiplication and division 
can be deduced as direct consequences from the theory 
of proportion as laid down by Euclid. 

(b) The Index Law. — Suppose P, Q to be two points 
moving in a straight line, the former with a velocity 
proportional to its distance from a fixed origin O, the 
. J P^^ vj 

latter with a constant velocity. I^et x represent the 
variable distance of P, y that of Q from the origin, and 
let A be the velocity of P when x=i, ^ the constant 
velocity of Q. The velocities that P will have acquired, 
as it arrives at the positions J, P', P", respectively, are 

A, x'\, x"\, 
and the corresponding values of x and y are 



52 Riverside Addresses. 

x=0^=i, ^'=-i+JF, x"=i-^]V'\ 

Q being supposed to pass the origin at the instant when 
P passes J, at which point ;r=OJ=i. The velocity of 
P, relatively to that of Q, is known, or vice versa, as 
soon as the ratio of yw to A is given. By means of this 
construction the terms modulus, base, exponential, and 
logarithm are defined as follows: 

(i) yu/A, a given value of which, say w, determines a 
system of corresponding distances x\ x" ^ ... andj/', 
y'\ ... is called the modulus of the system. 

(ii) The modulus having been assigned, the value 
of ;ir, corresponding to j/=OJ=i, is determined as a 
fixed magnitude, and is called the base of the system. 
We may denote it by b. 

(iii) x^ x\ x" . . . are called the exponentials of 7, 
y\ y\ . . . respectively, with reference to the base b^ 
and the relation between x and y is written 
x--=^b\ 

(iv) 7, j', 7" . . . are called the logarithms of x^ x\ 
x'\ ... respectively, with respect to the modulus m, 
and the symbolic definition is 

y=.\og^'^ X. 

Now, by virtue of definition (iii), 

.-. ^y'7<^^'==op'70P' 

-=i+p'p'70P'. 

But the magnitude i+P'P"/OP' represents the dis- 
tance that P would traverse, starting at unit's distance 
to the left of P', on the supposition that its velocity at 
P' is A;i;7^'= A, and the corresponding distance passed 
over by Q is f'^y'; hence by definition of the expo- 
nential, 

i+P'P'VOP'=^^" ^', 



Elementary Mathematics. 53 

and therefore 

which is the index law for a quotient. In particular, 
if/'=o, 

or \lb''=b~'\ 

and therefore writing —y'=y-, b^" I b^''=b^"~^' becomes 

which is the index law for a product. 

The addition theorem for logarithms, namely: 
log^-' (/"X/')=log^'"^/'+ log^V, 
may be proved in a similar manner from the figures, or 
it may be deduced as a consequence of the index law, 
and you will doubtless be willing to take my word for 
it that the law of involution 

{b''Y-={^b^Y=-b''^, 

together with its inverse logarithmic process 

h log x'^=k log x^=hk log x^ 
can be justified by the methods here described with 
equal facility. 

You will doubtless be interested to know that Napier's 
original definition of a logarithm was in its essentials 
the same as that I have just given. 

I must not tax your patience longer. If the thoughts 
I have chosen to la^^ before you this morning have not 
touched at many points the work that goes on in your 
school-rooms from day to day, I console myself with 
the hope that in 3^our own intellectual life outside the 
mathematical recitation-room some place may be found 
for the cultivation of your chosen subject as a science; 
for a thorough examination of its foundations, for a 
careful study of its history, and of the life-work of the 
men who have made it what it is. 



54 Riverside Addresses, 

I venture to predict that a judicious course of read- 
ing in mathematics would have many beneficial effects 
in your teaching. An anecdote concerning the man 
who first propounded 'Oa^pons asinoriim, or who discov- 
ered the binomial theorem, would be caught up by your 
pupils with eager interest. The great discoveries in 
science are comparable with the great crises in political 
history. By what principle in education do we teach 
our children to revere the names of lyconidas and War- 
ren, because they were the heroes of Thermopylae and 
Bunker Hill, but neglect to tell them to whom they 
are indebted for the knowledge made accessible to them 
in their arithmetic, their geometry, and their algebra? 
I recommend as subjects worthy of study and discus- 
sion in 5^our class-rooms, sketches in the history of 
mathematics. 



Physics in Secondary Schools. 55 



PHYSICS IN SECONDARY SCHOOLS. 

SOME ASPECTS OF THE PRESENT SITUATION. 
By Frederick Si.ate, 

Professor of Physics. 



In appearing before this gathering to-day, it is 
pleasant to bring with me the thought that conditions 
as regards high school work have become so much 
more favorable during the five years that have slipped 
by since I first made my appearance in this role; and 
in discussing physics-teaching, advocated the policy 
of making a permanent acquisition of our conceded 
share in secondary education through reform of method, 
and clear view of relation to other parts in the scheme 
of training. Such ameliorations as the present status 
shows are due, I am glad to be able to say, largely to 
continuous process, and not altogether to the stimulus 
which the acts passed by the last I^egislature applied. 

In the annual tour through the State, which has come 
to be an important part of my regular duty, the gaps 
between one high school and the next in which good 
work in all branches is turned out, are found to be 
closing up with every passing year. Vivid interest for 
the best ideas is keeping the workers astir in centers 
now numbering ten for one that was to be found five 
years ago; and physics has not lagged unduly behind 
the general front of the advance. 

The University of California made an early begin- 
ning, as compared with other institutions of like grade, 



56 Riverside Addresses. 

in laying down a requirement in physics for matricula- 
tion. This subject was introduced as alternative with 
chemistry or botany nearly ten years ago. In 1887 
free option among the group ceased, and since then 
physics has been exacted of all except matriculants 
upon the classical and literary requirements. During 
these later years, too, the examination-papers set, and 
what other influences could be exerted, were all con- 
sistently directed towards securing thoroughness of 
work, correctness of method, and wise selection of mate- 
rial. There is strong satisfaction in recognizing that 
the ideas of this kind which our State University 
championed from the outset, have, at this date, found 
general acceptance. "Where a concession is made to 
those who demand some science, * * * physics 
is the subject selected, because it includes more generic 
principles than any other science." This quoted sen- 
tence carries the authorit}^ of the committee report upon 
secondary education to the next meeting of the National 
Educational Association at Saratoga, in July, 1892. 

While, then, there is cause for self- congratulation; I 
mean with the secondary education of the State, not 
with the State University onlj^; it is nevertheless not 
to be lost sight of that the only mental attitude con- 
sistent with progress is that of cooperative inquir}^ and 
experiment, in order to sift out what may be regarded 
as established among the ideas and processes which 
have been tentativel}^ introduced into school-work; to 
recognize and adopt them, and thus, while we assure 
our foothold upon ascertained truth, to narrow down 
the field within which opinion needs to waver among 
uncertainties. It is equally inexpedient to look upon 
our problem as fully and permanently solved, or to think 
of ourselves as still merely upon the threshold of it. 



Physics in Secondary Schools. 57 

It may be profitable, therefore, as well as encouraging, 
if we here put down in brief summary some items in 
regard to which our position to-day is distinctly an 
advance as compared with that which we were com- 
pelled to occupy only a very few years ago. 

First, then, we need no longer to be clamorous 
about the importance of natural science in general or 
physics in particular. For causes apparent to most of 
us, some of which will be alluded to in another con- 
nection presently, several features of this work as done 
in schools have made such strong appeal to popular 
appreciation, that the various authorities have been 
easily led to grant freely what has been so unanimoush^ 
demanded. There was a time when I was obliged to 
plead for ph3^sics; but our present effort can be turned 
to making wise use of that which is the fruit of old- 
time exertions. 

In the second place, the broader features of the 
methods most appropriate to the study have been stated 
and generally agreed upon. If some older ones of us 
call up in memory the da^^s when we studied natural 
philosophy as we learned our catechism — b}^ question 
and answer laid down, and without a vestige of direct 
reference to the realities to which these statements 
applied — such memories but swell the tide of humorous 
pity for the methods in which the earlier generations 
were schooled; methods so perverse, according to all 
psychology and wider view of life, that we are reduced 
to wonder how so excellent a body of men and women 
could have been shaped in so bad a mold. 

And again, the benefits of what we rightly call reform 
in secondary education have accrued to our branch of 
study as well as others. We have cut down the num- 
ber of subjects taken up, and devoted a larger fraction 



58 Riverside Addresses, 

of the pupil's time to each; nor is there reasonable 
doubt that we shall find advantage in continuing 
this process beyond any point yet attained. In so 
doing we gain opportunity to impart what I call 
serious knowledge; to develop each branch to the 
degree necessary for making permanent impression 
upon young brains; and to lift ourselves out of the 
slough of superficialness into which high schools have 
been brought by a course of study touching upon 
almost all sides of learning. 

Indirectly, too, we are helped by the demand this 
thoroughness in what is taught makes upon the one 
who teaches. In a course laid down according to 
modern ideas, there is no place for any except those 
well-trained and fully-prepared to teach sound knowl- 
edge on the lines of good methods. 

With place assured, plans well outlined, and an 
emphatic demand for excellence of instruction, we 
have within reach good leverage for further progress; 
and we must not shrink from the weighty responsibil- 
ity of keeping our " intellectual conscience " awake in 
its search for still better things, and of conforming our 
practice to them as soon as found. 

What I have further to say is to be thought of as 
my endeavor to formulate for myself and for you the 
truth about what are now either (i) unclearly-held 
views, or (2) false tendencies, needing to be combatted, 
or (3) elements worthy of being included in our teach- 
ing. 

It is altogether likely, indeed, that some of you have 
heard from me, on various occasions and disconnectedly, 
all that the allotted time allows me to bring forward 
here. Nevertheless, the more public utterance and 
discriminating statement seem to offer advantages 
which warrant what may be introduced of repetition. 



Physics hi Secondary Schools. 59 

For some years past, we may even say ever since its 
introduction as a feature of school-work, the laboratory 
has offered themes fruitful of thought, and fruitful of 
discussion because of divergence in thought. It will 
be a distinct gain if we may contribute aught to-day 
towards fixing the scope and limitations of laboratory 
work, so that we are able to say of its field of useful- 
ness: '' It lies thus and so, and is hedged by these plain 
boundaries." If we can in any fair measure accom- 
plish this, there will follow clearer insight into the 
reason for its existence as a feature of science- teaching 
at the elementary stage; better judgment as to its 
necessity or indispensableness. 

It would not surprise me greatly to discover a num- 
ber present holding a discussion of these points to be 
a veritable threshing of chaff; but the very diversity of 
opinion and practice proves them undecided now, nor 
would it be anything unique if we should find that 
they had never been clearly thought out by many of 
those who zealously take part in introducing the labo- 
ratory system. For it is rather characteristic of the 
early stages in reform movements, that the rank and 
file at least are, in the literal sense of the word, 
adherents, and cleave to the view which happens their 
way, while the privilege of holding conviction as the 
result of thinking, and at the same time making it the 
basis of action, is reserved to the few who are akin to 
the generations following that in which their lot is cast. 

It would be to some extent true, I am sure, if we 
should trace a partly imitative process, which found 
the University laboratory in existence with its function 
of research, modeled the college laboratory after it, and 
copied this feature into the school system, without 
pausing to verj^ clearly define how the original function 



60 Riverside Addresses, 

must be modified to suit the changed conditions. This 
is not said at random; I have been met on many occa- 
sions with distinct indications of this sequence. 

Now it is apparent that out of the school-laboratory 
comes no investigation, in the sense of "increase of 
ascertained truth." Rediscovery of truth by the pupil 
there may be; ought certainly to be, and to a large 
extent, we find maintained, and we shall revert to this 
before leaving the topic; but the function of the matured 
scientific worker does not yet come into action. 

In another direction there are signs of attempted 
alliance with entirely different tendencies. About three 
years ago the idea of manual training received a strong 
impetus; some projects were even entertained and 
discussed for engrafting it upon the common school sys- 
tem. Did we not note movements of attraction between 
laboratory and manual training shop? It would be 
wrong to deny the existence of common ground on 
which these two different ideas overlap. But coales- 
cence would not have been in the true interest of either, 
and we must all have been glad to see the danger fade, 
away. 

I spoke freely on this subject at the Sacramento 
meeting in 1888; if I make allusion to it here, it is for 
the purpose of illustrating how a thing may be, and 
yet those who are called upon to administer it be 
wrapped in mistiness as to its true mission. The well- 
balanced mind avoids confounding these matters, as the 
eye escapes the confusions of color-blindness; by having 
within it faculty for perceiving all primary elements, 
and distinguishing shades and tints as blendings of 
these in varied proportion. 

Well, if the essential of laboratory work in schools 
be not manual training, that is, apparatus building, and 



Physics in Secondary Schools. 61 

cannot be discovery of new truth, may it not perhaps 
be new discovery of truth? Shall the classes be so 
conducted that the pupils are — to put the extreme 
case — told to make an experiment, being left unin- 
formed how the result should fall out? I could quote 
very respectable authority for the criticism upon cer- 
tain books: "Their scheme is all wrong, because 
they tell the pupil beforehand what to expect." That 
the proposed plan quickens observation, cultivates the 
investigating habit of mind, and lends keen zest to old 
experiments, although the sweetness of discovery is 
but tasted with the tip of the tongue, and is, after all, 
only of the kind we see in our boys as they hang 
breathless over Ivanhoe or Robinson Crusoe — all this 
must be readily conceded by every candid mind. There 
is much that appeals to me in an inclusive view of 
education as a thinking again of the thoughts of the 
race; with many foreshortenings, to be sure; with ex- 
tensive elimination of periods of groping, and much 
redistribution of emphasis; but in the main a bringing 
into contact w4th the recorded thought of humanity. 
So, too, there is of necessity,, under circumstances as 
sketched above, much of that individual treatment for 
pupils which is a marked characteristic of best educa- 
tion; to be striven after at every point among the 
elements opposed to it which the handling of crowded 
classes entails. 

If we tone down the leading idea from rank extreme 
to somewhat of moderation, I can fancj^ such a charm- 
ing picture of wise teacher in the midst of alert pupils, 
each actively thinking for himself, and aided to the 
extent and in the wa}^ suggested by the obstacles that 
block his path, that I am willing to let this ideal of 
laboratory stand bright before us, undimmed by any 



62 Riverside Addresses. 

critical analysis. Pupils may be led from stepping- 
stone to stepping-stone with proper, half-dissimulated 
guidance, avoiding treacherous footholds, and thus 
springing nimbly and securely over many a gap where 
the path-finder stumbled and fell short. 

I^et our further consideration and argument, there- 
fore, be confined to examining what results may be 
gained by executing a plan like this, and seeing in 
how far, as well as in what directions, such procedure 
needs supplementing before the requirements of the 
case are fully met. An examination of this sort cannot 
but prove fruitful if its brings out the truth, uncon- 
sciously possessed it may be, which gives to our plans 
and ideas their real value — value often ascribed to 
widely different sources. 

The word " rediscovery " seems to me apt as suggest- 
ing a feature in the working of the pupil's mind akin 
to what we find historically true in the process of 
original discovery. I mean that the results obtained 
involve a large element of intuition, and are not con- 
clusive and unassailable, as they may become through 
later scrutiny and test. It is strikingly shown, as we 
follow the course of development in the work of men 
like Galileo, like Huyghens, like Mayer, even, how 
incompletely established certain most valuable results 
were at the date of their first announcement. As in 
Alpine climbing the leader on the rope is often obliged 
to content himself with precarious foothold and slippery 
grasp as he picks the way, while those behind him 
secure themselves in notches cut, so Newton's minute 
examination for accuracy is needed to confirm Galileo's 
results; Young's labors bring testimony in support of 
Huyghens's generalizations, and only through Joule's 
patient detail comparisons is full acceptance gained for 
Mayer's ideas. 



Physics in Secondary Schools. 63 

At the very best our pupils repeat upon a minute 
scale the experiences of the former group, not those of 
the names in the second. 

We hear much said of the '' inductive method," which 
is often understood in a way that may be characterized 
as pretending — with more or less truth admixed — that 
we do Jtot know; but, as a matter of fact, hypothesis 
generally precedes experiment, and we test in order 
to discover whether we do know. Jevons has clearly, 
and as I think justly, pointed out how essential to the 
real process is this rapid flashing back and forth between 
assumption and putting it to the proof. 

Have we not all in mind Faraday's form of stating 
the truth? '' You must tell me what I am expected to 
see," he said, "before I can know whether I see it 
or not." That is, the mind must be prepared by 
h5^pothesis; we must look at phenomena, not with 
dispersed bovine gaze, but with retinal-spot highly 
sensitized for the one thing among the mass which are 
in sight. Ability to prophesy is the criterion of true 
knowledge. The bearing of these remarks will be plain, 
I hope, when we remember that our young people are 
doing their work under similar conditions, and in addi- 
tion are limited by their feebler powers. 

We must not expect, then, that laboratory practice, 
even for a favored group, is going to emancipate from 
all reliance upon authority, and enable us to write as 
device: "Accept only what you have yourself worked 
out;" or even the modified form, "What j-ou have 
yourself thought out." By occupying such extreme 
positions, which are in reality untenable, we constrain 
ourselves into adopting for defense controversial meth- 
ods, and losing that candor of mind which lies open to 
the truth. 



64 Riverside Addresses. 

In the light of many years spent in teaching and 
thinking, it seems impossible to affirm that, try as we 
may, there can be eliminated from our teaching the 
element of acceptance upon authority. Beginners must 
continually take bearings as they advance, and find 
whether they are in the beaten path, as I am told the 
geological survey runs its traverse-lines with repeated 
adjustment to the previously established points of an 
accurate triangulation. And ought this element to be 
cast out root and branch as wholly bad? Is not the 
claim that it should based upon extreme reaction against 
preponderant dogmatism? It is true, rather, that a 
part of all sound education is to cultivate due reverence 
for the past, and esteem for the legacies handed on to 
us from its worthies. The great and the good have 
worked to little purpose, if we are to refuse their inherit- 
ance unless every coin of it has been tried upon each 
individual touchstone. Nor should we fail to see the 
artificialness of a system which sets up, within a small 
range and during a limited period, standards whose 
use cannot be extended in time or space to cover human 
life. It is true of mature men of widest power that they 
command with independent research a small arc only 
upon the circumference of knowledge. 

In entering this plea for a remainder of authoritative 
teaching, I am running a-tilt against no mere man of 
straw. It is unfortunately true that just such extrav- 
agant claims as are here implied are made for the kind 
of work that we are discussing, which tend to bring it 
into disrepute with heads clear enough to see the fallacy 
of the position assumed. Interest in the adoption of 
the best methods demands that we should avoid such 
extremes as have been held up for criticism. We accept 
the law of gravitation, or the law of reflection for light, 



Physics in Secondary Schools. 65 

or Ohm's law for electrical currents; in fact the great 
body of laws which constitute what may be called 
formal physics — laboratory- work of school grade can 
at most think consequences of these and try to real- 
ize them. As a recent writer has said (and I think 
his utterances are the best I have seen in print upon 
the subject, perhaps because they come in as inde- 
pendent corroboration of w^hat I have long held and 
preached): *"The laws and principles which have 
been most carefully studied by scientific men should 
be made the instruments, not the objects, of scientific 
research. The teacher should avoid, as far as possible, 
experiments w^hose ostensible object is to establish well- 
known facts, like the law of conservation of energy, 
the truth of which is not really in question. But the 
use of the experimental method, as an illustration of 
such laws, is not to be denied. It is only through the 
aid of definite examples that most persons can arrive at 
an understanding of physics." 

A trenchant blow is struck in these sentences, every 
phrase of which counts, against the central fallacy of 
much that is carried out in school-work as quantitative 
measurement. It cannot be regarded as proving the 
law; but it is a proving of the pupil; of his conscien- 
tiousness, definiteness of knowledge, and power to take 
pains. Here lies, indeed, the connecting link between 
manual training and laboratory work, especially of 
the quantitative kind. Curiously enough this bond 
attaches on what we may denominate the ethical side. 
The constructive use of principles or materials has a 
reactive high moral value when wrong figures, or errors 
cut out in wood or iron, bring us face to face with 
faults in knowing or executing. A shrewd friend said 

* Whiting, Physical Measurement, p. 599. 
5~A 



66 Riverside Addresses. 

to me many years ago, that, during the period when 
we are fostering the thinking faculty in the younger 
generation, those subjects are the best adapted tools, 
which give the most frequent and accessible check and 
control upon the results of their essays at thinking. 
This is the kernel of the truth, I am sure. It may be 
useful to the unification of our thought to see a large 
share of the educational value in such subjects as 
geometry lying within these lines. There we have 
flawless standards, it is true, in hypothetical assump- 
tions, whose discord or harmony with conclusion gives 
certain answer as to correctness of reasoning; but laws 
of physics involved in school work are scarcely behind 
geometrical axioms in practical freedom from doubt. 
I am mistaken if some of the readiness with which 
physics has been incorporated into our schemes of 
study is not due to the recognition that it furnishes a 
large and new available supply of such material. 

It seems true, in spite of the claim that science- work 
in schools is inductive (meaning exclusively so), that 
we must make allowance for the existence of a con- 
siderable element which offers the essential feature of 
deduction. Namely, that certain ideas are assumed; 
with a coloring of reason offered, to be sure, but nec- 
essarily without critical analysis, weighing, and discus- 
sion; and of these the pupil thinks a corollary and 
works it out experimentally. As far as this kind of 
mental exercise is concerned, there is little to choose 
between laboratory problem and one set in geometry. 

This connection leaves the door open to place a word 
in defense of qualitative experiments, which it is the 
present tendency to reject almost entirely. But the 
intuitive activity of the mind finds exercise chiefly in 
qualitative work. It is here that rediscovery, with its 



Physics in Secondary Schools. 67 

(rather fictitious) novelty, can be properly spoken of. 
I know that students in my own classes often show the 
onesidedness that is the fault of familiarity with those 
experiments exclusively which are emplo3'ed because 
they afford exact methods, while experiments are passed 
by that yield only views of connection between cause 
and effect in phenomena. In the school-years such 
exclusiveness is still less in place, so that this thought 
deserves of us that we bear it in mind and correct our 
practice by it. 

On gathering together what these considerations have 
thus far shown, we shall have before us the answer, as 
I conceive it, to the question which concerns itself with 
results to be expected of our ideal laboratory. Those 
who are subjected to its discipline may be guided to 
infer the qualitative statement of physical laws; they 
may experimentally learn to know what are the main 
determining causes of a wide range of phenomena. 
Their conclusions will be compared with established 
truth mainly, and their correct understanding of rela- 
tions will be brought out by measurements which 
involve the application of assumed quantitative laws. 
As bye-products they will have gained a fair degree of 
manipulative skill — manual dexterity, that is; and, if it 
be fair to call this a bye-effect, a set towards conscien- 
tious accuracy and the facing of facts that ramifies 
widely into the fibers of character. And all of this 
with healthful stimulus of interest and development of 
faculty upon the two great lines of inductive and 
deductive reasoning. 

We may be content to call this a goodly harvest, 
although our claims are modest by the side of those I 
have heard advanced. Training like this is desirable, 
and that although the actual profit-sheet may never 



68 Riverside Addresses. 

show as large dividends as these. Our minds are 
prepared to meet a coming-short of ideals in any edu- 
cational scheme as applied to a particular group of 
pupils; but it is of the highest importance to know 
whither our effort should tend, and to hold ourselves 
and our young charges up to aim for the very best. 

Another branch of our inquiry raises the issue 
whether such laboratory training is likely to be suffi- 
cient, or whether it needs supplementing. Experience 
seems to show that it does. I will \xy to present the 
matter through an analogy. The suggestion that 
comes from several parallel cases is of the same tenor, 
and we should heed it. Time was, when the study of 
the classics was prepared for by solid digging at the 
grammar, which was mastered by rote before any 
venture was made in reading the literature. This 
period was succeeded by a strong reactionary tendency 
to abolish the study of formal grammar, and to derive 
all such material from the text. It has been found, 
however, that the same high level of attainment cannot 
be reached if the grammar-book be dispensed with. It 
is introduced at a different stage, in less isolated fashion, 
with larger proportion of text-reading, and truer expo- 
sition of the principles of grammar, as inferred from the 
observed phenomena of the language used; but no 
substitute completely replaces it. 

I hope for the day when the school-grammar of 
physics shall be wisely written, fully mastered in con- 
nection with our reading of the text, which is Nature, 
with proper understanding of the statement of formal 
law as general truth obtained by collation of phenomena. 
We have had our days of rote-learned grammar; we 
have had our phase of undue reliance upon text-reading 
and consequent slovenliness. Perhaps better things 
lie just ahead. 



Physics in Secondary Schools. 69 

There is at the present time a well-marked drift 
towards removing- difficulty from the pathwa}^ to 
knowledge, which gives a kind of general support to 
the belief which has spread abroad in regard to labora- 
tory^ methods, that they make subjects entertaining to 
the degree of being learned as play. There should be 
rejoicing over the disappearance of those difficulties 
which have their source in allowing the end to be 
eclipsed behind the means to the end, in perverse 
routine, and the whole apparatus of pedantry; that evil 
spirit whom we should all be glad to know of as exor- 
cised from our school-rooms forever. But clearing away 
this rubbish does no more than render it possible to 
concentrate effort upon the real inherent resistance of 
the subject, as the felling of a tree is facilitated by 
removing the brush which deadens the axe-blows. 
Difficulty must continue to meet those who attack 
whatever possesses sterling educational value; it is, in 
fact, one stamp in the hall-mark. 

I do most sincerely maintain that we should put 
work before our 3'oung people which requires effort, 
strenuous effort, in order to accomplish the tasks set. 
We must continue to place a high value upon the 
years of adolescence; the period of rapid expansive 
growth and strong assimilating power for mind as well 
as body; the time during which the habit of consecu- 
tive effort should become ingrained. We can do no 
better service to pupils nearing the end of their high 
school course, than to claim and gain for them leisure 
to satisfy the requirement of thinking, and growing 
strong in controlled power to think, while we discour- 
age nervous cram and sham acquisition. 

If, then, to turn from general statement to the matter 
in hand, there are, as I have tried to show, needs for 



70 Riverside Addresses. 

systematic knowledge of principles, rooted in the sub- 
ject-matter; existing, not as alternative to laboratory- 
work, but as condition that an important part thereof 
may be successfully prosecuted; it is acting in the 
interest of the pupil if we do not shirk the task thus 
imposed, of encountering a citadel of difficulty transcend- 
ing those met in the recreative experimental outworks. 
We are thus helping to inculcate the lesson which is 
the quintessence of so many lessons; that is, in Hux- 
ley's words: " The most valuable result of all education 
is the ability to make yourself do the thing you have 
to do, when it ought to be done, whether you like it or 
not. * * * However early a man's training begins, it 
is probably the last lesson that he learns thoroughly." 

Our newest text-books do not help us as they might 
just here. Their abstruseness has been largely toned 
down by the wholesome and clarifying influences of 
experimental exercises. So much thought is excited 
by what is taken in hand, and so much explanation 
called for of every-day occurrences, that the elimination 
of advanced theories may be relied upon to work almost 
automatically. We can, if necessary, aid this process by 
judicious omissions; but the lax incoherency of some 
of our books is not so easily neutralized. 

We are all aware that text-books are by no means 
mirrors reflecting opinion current among experienced 
teachers; so it would be unfair to judge practice by 
them. All teachers, and the best teachers most of all, 
make discriminating use of their books, to the extent 
often of recasting the matter in presentation. But 
print is powerful, and not yet altogether divested of 
sacredness; the molding influence of the book, too, is 
felt most strongly by those very younger members of 
the profession upon whose development it is most 



Physics ill Secondary Schools. 71 

urgent to impress the right direction. It seems per- 
missible, therefore, that I should devote to criticism of 
our text-books a few further words, which are a protest 
against the lack of proportion in their treatment of 
topics ; and in sa34ng this I have electricity quite promi- 
nently before my mind. It may look paradoxical to 
raise outcry against magnifying those applications of 
physics which have brought an influx of students — 20 
for I fifteen years ago — and have unlocked coffers for 
the building of laboratories, besides forming the " crown- 
ing success of the century," as they have harnessed a 
new form of energy in the service of man. Such plea 
comes with all the more force and temptation, because 
the time in which we are sits dazzled under the sway 
of electricity. We no longer realize perspective in 
these things; but physics is in danger of being swamped 
by the unexampled material success in this one of its 
divisions, as an examination of our colleges easily 
shows. And so in the schools, possession is taken of 
our books from the early pages, in which centimeter- 
gram-second system is forced upon pupils unable to 
comprehend it, to the Volt, Ampere, Wheatstone bridge, 
and other members of the goodly company that bring 
up the rear. 

Application of principle to cases occurring in daily 
life meets with my strongest approval. I can say, in 
the simple words of Maxwell: 

* " Science appears to us with a very different aspect 
after we have found out that it is not in the lecture- 
room only, and by means of the electric light projected 
on a screen, that we may witness physical phenomena, 
but that we may find illustrations of the highest doc- 
trines of science in games and gymnastics, in traveling 

* Scientific papers, Vol. II, p. 243. 



72 Riverside Addresses. 

by land and by water, in storms of the air and of the 
sea, and wherever there is matter in motion. 

"This habit of recognizing principles amid the end- 
less variety of their action can never degrade our sense 
of the sublimity of nature, nor mar our enjoyment of 
its beauty. On the contrary, it tends to rescue our 
scientific ideas from that vague condition in which we 
too often leave them, buried among the other products 
of a lazy credulity, and raise them into their proper 
position among the doctrines in which our faith is so 
assured that we are ready at all times to act upon 
them." 

But when one most modern application is seen over- 
shadowing all others with a predominance due to 
evanescent causes, I feel we are making a blunder if 
we yield to the pressure. For physics is the classic 
among the sciences; it forms the permanent record of 
man's success in accumulating, through centuries of 
effort, a reasoned explanation of large groups of phe- 
nomena. Instead of reserving chief emphasis for the 
most modern contributions, and thus ignoring an oppor- 
tunity, which is so plainly ours, of casting off the 
reproach urged against science; that it is lacking in the 
human element; we should aim at bringing out the 
historical aspect of discoveries as they come up for 
treatment, beyond the mere uncommented mention of 
a name, and at exciting lively interest in this picture 
of international cooperation upon an edifice which has 
been building through more centuries than Cologne 
cathedral, and which is more imposing to the mental 
vision, although less substantial than stone and mortar. 
I recommend to you sketches from the history of 
physics as valuable material for the class-room — well 
adapted to enforce the lessons most desirable to impress; 



Physics in Secondary Schools. 73 

of painstaking slow advance, and hard work over every 
inch of conquered ground. 

At several points in what precedes, I have implied 
the close relation among the several branches of high 
school work by insisting upon the results of comparing 
them in parallel. Before bringing these remarks to a 
close, I should like to urge this idea more explicitly, as 
its value deserves. 

The task of the public school on the intellectual side 
may be considered as being to : ( i ) Impart useful 
knowledge; (2) Promote clearness of thought; (3) 
Cultivate accurate expression. We should find earnest 
striving after these three things in every class-room. 
Where this is the case with studies in language, math- 
ematics, and science, each pair buttresses the third, and 
the unity of purpose sets its stamp upon the pupil's 
mind. 

For reasons connected mainly with the need of 
imparting varied and extended information, we segre- 
gate into separate class-rooms, and place in charge of 
teachers specially qualified to handle and expound por- 
tions of the material which it is advisable to treat. Yet, 
after all, in our thought and in their essence, these are 
but fractions of a unity ; these comings and goings and 
modulations of key can be grouped into a harmony of 
movement and of utterance for one central theme. 

Last Spring, an eminent preacher and lecturer devel- 
oped for me, in conversation, the idea that all our out- 
door sports are wrong in principle, because they involve 
a striving of one, or of one crew, for victory, which 
must also mean defeat. The truer human end would 
be reached, he maintained, by including in one effect 
the efforts of all, combined with proportion and rhythm. 
There is perhaps too much of the Anglo-Saxon in me 
6— A 



LIBRARY OF CONGRESS 



74 



Riverside Addresse. 




019 810 607 



to quite accept this view as to fie 

not convinced that rivalr}^ in contest is not succeeded 

by generosity in those who excel, ungrudging praise 

in those who are proved inferior. But within the 

range of education I can find deep truth in this view, 

and do regard it as bringing to utterance soundest 

doctrine. 



LIBRARY OF CONGRESS 



019 810 607 C 



